arXiv subjects

Danilo S. Jodas

Publications and source records attributed to Danilo S. Jodas.

3 recordsLinked to original sources

arXiv2026

PUBO Formulation for MST and Application to Optimum-Path Forest

The Optimum-Path Forest is a graph-based framework for designing classifiers that exploit inter-sample connectivity. A particular variant constructs decision boundaries based on prototypes computed by a Minimum Spanning Tree (MST) over the training data, which might become prohibitive for large-scale datasets. In this context, Quantum Machine Learning has emerged as a promising approach to overcome the high computational burden of combinatorial problems. We propose a quantum-inspired approach for prototype selection in OPF classifiers by reformulating the MST problem as a Polynomial Unconstrained Binary Optimization (PUBO) task and further employing the Feedback-Based Quantum Optimization (FALQON) algorithm for Hamiltonian minimization. The PUBO formulation reduces the need for qubits and eliminates the need for auxiliary variables, thereby addressing scalability constraints in current quantum hardware. Experiments on real-world datasets demonstrate that the FALQON-optimized MST achieves accuracies comparable to those of the classical Prim's algorithm while maintaining prototype quality. While FALQON occasionally reached local minima, it did not significantly impact the accuracy of the prototype selection process.

quant-ph↗

arXiv2026

FALQON-MST: A Fully Quantum Framework for Graph Optimization in Vision Systems

Finding the minimum spanning tree (MST) of a graph is an important task in computer vision, as it enables a sparse and low-cost representation of connectivity among elements (such as superpixels, points, or regions), which is useful for tasks such as segmentation, reconstruction, and clustering. In this work, we propose and evaluate a fully quantum pipeline for computing MSTs using the FALQON algorithm, a feedback-based quantum optimization method that does not require classical optimizers. We construct a Hamiltonian formulation whose ground-state energy encodes the MST of a graph and compare different FALQON strategies: (i) time rescaling (TR-FALQON) and (ii) multi-driver configurations. To avoid domain-specific biases, we adopt graphs with random weights and show that the FALQON variants exhibit significant differences in ground-state fidelity. We discuss the relevance of this approach for computer vision problems that naturally yield graph representations, and experimental results on synthetic instances together with a small demonstrative study on image segmentation illustrate both the potential and the current limitations of the method. Our numerical simulations on randomly weighted graphs show that standard one drive FALQON, although it reduces the expected energy, fails to concentrate amplitude in the MST solution. The multi drive variant succeeds in redistributing probability mass toward the ground state so that the MST appears among the most probable outcomes, and TR FALQON applied over multi drive produces the best results with faster convergence, lower final energy, and the highest solution state probability or fidelity in our tested instances. These improvements were observed on small synthetic graphs, underscoring both the promise of multi drive controls with temporal rescaling and the need for further scaling and hardware validation.

quant-ph↗

arXiv2022

Handling Imbalanced Datasets Through Optimum-Path Forest

In the last decade, machine learning-based approaches became capable of performing a wide range of complex tasks sometimes better than humans, demanding a fraction of the time. Such an advance is partially due to the exponential growth in the amount of data available, which makes it possible to extract trustworthy real-world information from them. However, such data is generally imbalanced since some phenomena are more likely than others. Such a behavior yields considerable influence on the machine learning model's performance since it becomes biased on the more frequent data it receives. Despite the considerable amount of machine learning methods, a graph-based approach has attracted considerable notoriety due to the outstanding performance over many applications, i.e., the Optimum-Path Forest (OPF). In this paper, we propose three OPF-based strategies to deal with the imbalance problem: the $\text{O}^2$PF and the OPF-US, which are novel approaches for oversampling and undersampling, respectively, as well as a hybrid strategy combining both approaches. The paper also introduces a set of variants concerning the strategies mentioned above. Results compared against several state-of-the-art techniques over public and private datasets confirm the robustness of the proposed approaches.

cs.LG↗